The present invention relates to a method and system for creating three-dimensional displays or images from a multiplicity of two-dimensional projections and, more specifically, to a method and system for use in computed tomography systems in which random relative positional geometries between the source of radiation, the object of interest, and the recording means may be used for recording radiographic images for tomosynthesis.
A wide range of tomosynthetic imaging techniques has previously been demonstrated to be useful in examining three-dimensional objects by means of radiation. These imaging techniques differ in the size and configuration of the effective imaging aperture. At one extreme, the imaging aperture approaches zero (i.e., a pinhole) and the resulting display is characterized by images produced from a single transmission radiograph. This yields an infinitely wide depth of field and therefore no depth information can be extracted from the image. At the other extreme, the aperture approaches a surrounding ring delimiting an infinite numerical aperture resulting in projection angles orthogonal to the long axis of the irradiated object. This yields an infinitely narrow depth of field and hence no information about adjacent slices through the object can be ascertained. It therefore follows that a xe2x80x9cmiddle groundxe2x80x9d approach, which provides the ability to adapt a sampling aperture to a particular task, would be highly advantageous.
The key to achieving the full potential of diagnostic flexibility lies in the fact that perceptually meaningful three-dimensional reconstructions can be produced from optical systems having any number of different aperture functions. That fact can be exploited since any aperture can be approximated by summation of a finite number of appropriately distributed point apertures. The key is to map all incrementally obtained projective data into a single three-dimensional matrix. To accomplish this goal, one needs to ascertain all positional degrees of freedom existing between the object of interest, the source of radiation, and the detector.
In the past, the relative positions of the object, the source, and the detector have been determined by fixing the position of the object relative to the detector while the source of radiation is moved along a predetermined path, i.e. a path of known or fixed geometry. Projective images of the object are then recorded at known positions of the source of radiation. In this way, the relative positions of the source of radiation, the object of interest, and the detector can be determined for each recorded image.
Previously, a method and system has been described which enables the source of radiation to be decoupled from the object of interest and the detector. This is accomplished by fixing the position of the object of interest relative to the detector and providing a fiducial reference which is in a fixed position relative to the coupled detector and object. The position of the image of the fiducial reference in the recorded image then can be used to determine the position of the source of radiation.
However, none of the existing techniques can be used in the most general application wherein the radiation source, the object of interest, and the detector are independently positioned for each projection. In such systems, there are nine possible degrees of freedom: 2 translational and 1 displacement degrees of freedom for the radiation source relative to the selected object and 2 translational, 1 displacement, 2 tilting, and 1 rotational degrees of freedom for the recording medium relative to the selected object. It is highly desirable to have a system and a method for constructing a three-dimensional radiographic display from two-dimensional projective data wherein the source of radiation, the object of interest, and the detector are all allowed to independently and arbitrarily vary in position relative to each other.
The present invention relates to an extension of tomosynthesis which facilitates three-dimensional reconstructions of an object from any number of arbitrary plane projections of the object produced from any number of arbitrary angles. The information required to produce the three-dimensional reconstructions is derived from fiducial analysis of the projection themselves or from analyses of functional relationships established through known fiducial constraints. In accordance with the present invention, a system and methods are provided for creating three-dimensional images using tomosynthetic computed tomography in which the system and methods significantly simplify the construction of image slices at selected slice positions through an object. Following a one-time transformation of a series of projected images, only simple offset and averaging operations are required in selected embodiments of the invention for a variety of subsequent reconstructions of a volumetric region within which projective variations may be considered negligible.
The system comprises an identifiable fiducial reference located in a fixed position relative to the object. The fiducial reference comprises at least two reference markers which are in a fixed geometry relative to each other. One of the reference markers may be used as an alignment marker during construction of a tomosynthetic slice through the object. The other reference marker or markers may be used to projectively warp or transform a projected image from an actual projection plane to a virtual projection plane. Each reference marker may be small enough to be considered point-size or, alternatively, may be finite in size. However, there are advantages to using markers of a known geometry such as spherical markers with a measurable diameter. In one embodiment, the fiducial reference comprises five point-size or finite reference markers that are arranged so that four of the reference markers are co-planar and no three or more reference markers are collinear.
A radiation source is provided for irradiating the object with the fiducial reference in a fixed position relative to the object. The preferred radiation source depends upon the particular application. For example, the present invention may be practiced using x-rays, electron microscopy, ultrasound, visible light, infrared light, ultraviolet light, microwaves, or virtual radiation simulated by manipulation of magnetic fields (magnetic resonance imaging (MRI)).
A recording medium or detector is used to record a series of projected images. Each projected image may include an object image of the object and a reference marker image for each of the reference markers. The recording medium may be in the form of a photographic plate or a radiation-sensitive, solid-state image detector such as a charge-coupled device (CCD), or any other system capable of producing two-dimensional projections or images suitable for digitization or other analysis.
In operation, the system of the present invention is used to synthesize a three-dimensional reconstruction of the object to obtain, for example, an image slice through the object, at a selected slice position through the object, from a plurality of projected images detected at the recording medium. The simplification of the construction method is achieved by warping, i.e. transforming or mapping, a series of projected images onto a virtual projection plane to yield modified images that would match those that would have been generated had the detector been in a fixed position relative to the object. By warping the projected images onto the virtual projection plane, the computation required for each image slice construction is greatly reduced. In addition, the solution of the projective transformations can be performed via a direct method that is both efficient and computationally robust. Further, magnification differences can be compensated for by appropriate scaling of the images.
A series of two-dimensional projected images of an object with an associated fiducial reference is recorded. The fiducial reference markers are coupled in fixed position relative to the object. The projected images can be recorded with (i) the source, (ii) the recording medium, and (iii) the fiducial reference markers coupled to the object, in various or arbitrary projection geometries. Further, the projection geometry preferably varies from projected image to projected image. Some variation is required to produce a finite depth of field.
The virtual projection plane may preferably correspond to the position of a plane through at least one of the reference markers in real space or to a plane defined by one of the existing projected images. Imaging systems that use projective geometries, which include optical and radiographic systems, can be appropriately warped using a projective transformation matrix. The projective transformation matrix is generated by solving each projected image relative to the virtual projection plane.
The resulting transformations compensate for magnification and/or projective differences between the various images. Such differences are introduced when the source is sufficiently close to the object and/or the source moves in a direction which is not parallel to the projection plane.
Once the projected images are warped and scaled to compensate for projective artifacts, construction of an image slice of the object at a selected slice position is performed based on techniques used in single reference marker applications. An example of such a technique is described in U.S. Pat. No. 5,359,637, which is incorporated herein by reference. Accordingly, the single reference point projection required by this technique may be abstracted from characteristics known to be associated with the object being projected, or from one or more fiducial reference markers either attached to or otherwise functionally related to the irradiated object.